Abstract
A HIV-1 model with two distributed intracellular delays and general incidence function is studied. Conditions are given under which the system exhibits the threshold behavior: the disease-free equilibriumE0is globally asymptotically stable ifR0≤1; ifR0>1, then the unique endemic equilibriumE1is globally asymptotically stable. Finally, it is shown that the given conditions are satisfied by several common forms of the incidence functions.
Highlights
The global stability is analyzed for a general mathematical model of HIV-1 pathogenesis proposed by Nelson and Perelson [1]
There are some pieces of evidence showing that a bilinear infection rate might not be an effective assumption when the number of target cells is large enough
The global properties were studied in [12, 13]
Summary
The global stability is analyzed for a general mathematical model of HIV-1 pathogenesis proposed by Nelson and Perelson [1]. The aim of this paper is to establish global stability for a delay integrodifferential equation with a general incidence term f(x, V), the conditions given here are similar to those given in [4] for the ODE case. We consider the following HIV-1 model with a side class of nonlinear incidence rates and distributed delays: dx (t) dt. As shown, many commonly used incidence functions satisfy these conditions. In. Section 5, examples are given of incidence functions which satisfy the assumptions that are used throughout the paper
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